Who Will Win the Coin Toss on Sunday? Ask PTC Mathcad

Written By: Dave Martin
  • Math Software
  • 1/31/2018

The coin toss that starts the big game on Sunday is one of the most popular “propositions” around. A “proposition” or “prop” speculates on the occurrence of an event during a game that doesn’t directly affect the game itself. For example, you can take sides with friends on which team scores first, whether either team will make a fourth down conversion, or how long Pink will sing the word “Braaaaaave” during the National Anthem. Propositions on the coin toss (you can find the rules here) are popular because you have a 50-50 chance of being right, and it requires absolutely zero sports knowledge.

 Football sits on field

Does the coin toss have any correlation to the outcome of the game? Anytime that you have data is a great opportunity to use PTC Mathcad to crunch the data and investigate relationships and trends. Let’s dive in!

Getting Started

The NFL championship game is the most popular sporting event in the United States. It accounts for the top 8 most watched programs of all time, and 19 of the top 20. (The finale for M*A*S*H is number 9.) You would think it would be easy to find data regarding the coin toss. You would be wrong.

After a bunch of Google searches, I found enough information to start crunching the numbers. I entered the following data into a spreadsheet: year, visiting conference (NFC or AFC), visiting team, call of the coin toss, result, coin toss winning team, coin toss winning conference, game winner, and game winning conference.

 spreadsheet with football coin toss data

Now it’s off to PTC Mathcad!

Import Spreadsheet and Basic Analysis

The first step is to import the spreadsheet using the ReadExcel function:

 importing spreadsheet into PTC Mathcad

It imports as a matrix, but I’m going to turn individual columns into vectors:

 Process matrix into vectors

Let’s perform some basic counting and statistics:

 basic counting and stats

The number of times teams call Heads or Tails is about even, with tails getting called 51% of the time. Tails has landed 52.9% of the time. These ratios fall within one standard deviation of the mean, so no surprises so far.

Programming with PTC Mathcad

Let’s look at how many times the visiting team has called the coin toss correctly. To do so, I’m going to use PTC Mathcad’s programming functionality:

 times called correctly

The function CalledCorrect takes two vectors as inputs. The program initializes a counter variable, and executes a for-loop to cycle through the records. The loop compares the coin toss call with the actual result. If they are the same, the counter increments. The visiting team has called the coin toss correctly 28 times - still within one standard deviation.

For giggles, how many times has Heads been called correctly? A similar program has nested if-statements to check if Heads was called before comparing the call to the result:

 how often heads called correctly NFL coin toss

Heads was the correct call 13 out of the 28 correct calls, which is 46.4%. Still no surprises.

Let’s turn our attention to the game results. How many times has the visiting team won, regardless of the coin toss? Our new program compares the vector of visiting teams to the vector of winning teams:

 how often visiting team wins football championship

Here is our first shocking result! The visiting team has won the game 30 times (58.8%), compared to the home team’s 21 victories. Wow!

This certainly bodes well for Philadelphia. Fly, Eagles, fly!

Stay Tuned!

We’re not done yet. There’s more to dissect. In our next installment, we’ll look at the following:

  • How does making the correct call correlate to winning the big game?
  • How the 2008 rule change has affected the past nine championship games.
  • The anomalies in the coin toss, especially in recent history.
  • At least two more shocking results from the coin toss analysis.

Enjoy the Big Game, and may victory finally be yours, my beloved Philadelphia Eagles!!!

 Want to see my spreadsheet and PTC Mathcad worksheet? Drop me a line at dmartin@creowindchill.com and I’ll send them to you!

Want to try the math for yourself?  Download PTC Mathcad Express for free. 

download mathcad express free

  • Math Software

About the Author

Dave Martin

Dave Martin is a former Creo, Windchill, and Mathcad instructor and consultant. After leaving PTC, he was the Creo specialist for Amazon; and a mechanical engineer, Creo administrator, and Windchill administrator for Amazon Prime Air. He holds a degree in Mechanical Engineering from MIT and currently works as an avionics engineer for Blue Origin. 

Martin is the author of the books Design Intent in Creo Parametric and Top Down Design in Creo Parametric--both available at www.amazon.com. He can be reached at dmartin@creowindchill.com.